Convection currents in a porous medium form when the medium is subject to sufficient heating from below (or equivalently, cooling from above) or when cooled or heated from the side. In the context of geothermal energy extraction, we are interested in how the convection currents transport heat when a sealed borehole containing cold fluid extracts heat from the porous medium; also known as a borehole heat exchanger. Using pseudospectral methods together with domain decomposition, we consider two scenarios for heat extraction from a borehole; one system where the porous medium is initialized with constant temperature in the vertical direction and one system initialized with a vertical temperature gradient. We find the convection currents to have a positive effect on the heat extraction for the case with a constant initial temperature in the porous medium, and a negative effect for some of the systems with an initial temperature gradient in the porous medium: Convection gives a negative effect when the borehole temperature is close the initial temperature in the porous medium, but gradually provides a positive effect if the borehole temperature is decreased and the Rayleigh number is larger.
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